AmesHw
Zoe Zenker
2025-04-17
Introduction
This analysis aims to predict residential sale prices in Ames, Iowa using a linear regression model with four key predictors. I will focus on variables that reflect size, location, and condition of the properties.*
Method
##
## Call:
## lm(formula = sale_price ~ log_gr_liv_area + clean_quality + year_built +
## neighborhood, data = t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -216317 -26532 -1904 17989 408433
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.475e+06 7.662e+04 -32.298 < 2e-16 ***
## log_gr_liv_area 1.345e+05 2.773e+03 48.511 < 2e-16 ***
## clean_quality 4.386e+02 1.198e+03 0.366 0.714234
## year_built 8.497e+02 3.886e+01 21.867 < 2e-16 ***
## neighborhoodEdwards -1.755e+04 4.568e+03 -3.841 0.000125 ***
## neighborhoodNorth_Ames -4.806e+03 3.825e+03 -1.256 0.209049
## neighborhoodNorthridge_Heights 7.669e+04 4.561e+03 16.816 < 2e-16 ***
## neighborhoodOld_Town -4.436e+03 4.986e+03 -0.890 0.373627
## neighborhoodSomerset 9.737e+03 4.390e+03 2.218 0.026652 *
## neighborhoodOther 6.377e+02 3.202e+03 0.199 0.842136
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 45490 on 2920 degrees of freedom
## Multiple R-squared: 0.6767, Adjusted R-squared: 0.6758
## F-statistic: 679.2 on 9 and 2920 DF, p-value: < 2.2e-16Model Performance
## RMSE: 45411.99## R-squared: 0.6767485Residuals & Plot
Key Findings
- LogGrLivArea: Homes with more living space tend to have higher prices. Using the log scale improved the linearity and model performance.
- OverallQual: As expected, overall quality is strongly correlated with sale price. Each increase in quality score increases price significantly.
- YearBuilt: Newer homes are generally more expensive, showing the impact of modern construction and updated features.
- Neighborhood: Neighborhoods differ significantly in pricing, even after controlling for size and quality. Location matters.
Conclusion
Our model achieved an R^2 of 0.6767485 and RMSE of 45411.99, which suggests a fairly strong predictive power using only four variables. The results affirm that size, quality, age, and neighborhood are key drivers in housing prices.